{"paper":{"title":"Covering Metric Spaces by Few Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Nova Fandina, Ofer Neiman, Yair Bartal","submitted_at":"2019-05-18T09:08:17Z","abstract_excerpt":"A {\\em tree cover} of a metric space $(X,d)$ is a collection of trees, so that every pair $x,y\\in X$ has a low distortion path in one of the trees. If it has the stronger property that every point $x\\in X$ has a single tree with low distortion paths to all other points, we call this a {\\em Ramsey} tree cover. Tree covers and Ramsey tree covers have been studied by \\cite{BLMN03,GKR04,CGMZ05,GHR06,MN07}, and have found several important algorithmic applications, e.g. routing and distance oracles. The union of trees in a tree cover also serves as a special type of spanner, that can be decomposed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07559","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}